更改

nodes and K=1 links per node. Nodes can be either switched on (red) or off (blue). Thin (black) arrows symbolise the inputs of the Boolean function which is a simple "copy"-function for each node. The thick (grey) arrows show what a synchronous update does. Altogether there are 6 (orange) attractors, 4 of them are fixed points.]]

nodes and K=1 links per node. Nodes can be either switched on (red) or off (blue). Thin (black) arrows symbolise the inputs of the Boolean function which is a simple "copy"-function for each node. The thick (grey) arrows show what a synchronous update does. Altogether there are 6 (orange) attractors, 4 of them are fixed points.]]

有多个节点，每个节点是K = 1个链接。 节点可以打开（用红色表示）或关闭（用蓝色表示）。 细（黑色）箭头表示布尔函数的输入，布尔函数是每个节点的简单“复制”函数。 粗（灰色）箭头显示同步更新的作用。 共有6个（橙色）吸引子，其中4个是固定点。

节点和每个节点K=1条链路。节点可以被打开（红色）或关闭（蓝色）。细（黑色）箭头象征着布尔函数的输入，布尔函数是每个节点的简单 "复制 "函数。粗（灰色）箭头表示同步更新的功能。总共有6个（橙色）吸引子，其中4个是固定点。

 

A Boolean network consists of a discrete set of boolean variables each of which has a Boolean function (possibly different for each variable) assigned to it which takes inputs from a subset of those variables and output that determines the state of the variable it is assigned to.  This set of functions in effect determines a topology (connectivity) on the set of variables, which then become nodes in a network. Usually, the dynamics of the system is taken as a discrete time series where the state of the entire network at time t+1 is determined by evaluating each variable's function on the state of the network at time t.  This may be done synchronously or asynchronously.

A Boolean network consists of a discrete set of boolean variables each of which has a Boolean function (possibly different for each variable) assigned to it which takes inputs from a subset of those variables and output that determines the state of the variable it is assigned to.  This set of functions in effect determines a topology (connectivity) on the set of variables, which then become nodes in a network. Usually, the dynamics of the system is taken as a discrete time series where the state of the entire network at time t+1 is determined by evaluating each variable's function on the state of the network at time t.  This may be done synchronously or asynchronously.

'''<font color="#FF8000">布尔网络 Boolean Network </font>由一组离散的布尔变量组成，每个布尔变量都分配有一个布尔函数（每个变量可能不同），该布尔函数从这些变量的子集中获取输入，并确定变量所分配到的状态 。 这组功能实际上确定了变量集上的拓扑（连接性），这些变量随后成为网络中的节点。 通常，系统的动力学被视为离散的时间序列，其中在时间t + 1时整个网络的状态是通过评估在时间t时网络状态的每个变量的功能来确定的。 这可以同步或异步完成。

'''<font color="#FF8000">布尔网络 Boolean Network </font>由一组离散的布尔变量组成，每个变量都被分配了一个布尔函数（可能每个变量都不同），它从这些变量的子集中获取输入，并输出决定其被分配的变量的状态。 这一组函数实际上决定了变量集上的拓扑结构（连通性），这些变量就成为网络中的节点。通常，系统的动态是以离散时间序列的形式进行的，通过评估每个变量在时间t的网络状态上的函数来确定整个网络在时间t+1的状态，这可能是同步或异步完成的。

Boolean networks have been used in biology to model regulatory networks. Although Boolean networks are a crude simplification of genetic reality where genes are not simple binary switches, there are several cases where they correctly capture the correct pattern of expressed and suppressed genes.  

Boolean networks have been used in biology to model regulatory networks. Although Boolean networks are a crude simplification of genetic reality where genes are not simple binary switches, there are several cases where they correctly capture the correct pattern of expressed and suppressed genes.  

The seemingly mathematical easy (synchronous) model was only fully understood in the mid 2000s.<ref name=DrosselRbn>{{cite book|last1=Drossel|first1=Barbara|editor1-last=Schuster|editor1-first=Heinz Georg|title=Chapter 3. Random Boolean Networks|date=December 2009|doi=10.1002/9783527626359.ch3|arxiv=0706.3351|series=Reviews of Nonlinear Dynamics and Complexity|publisher=Wiley|pages=69–110|isbn=9783527626359|chapter=Random Boolean Networks}}</ref>

The seemingly mathematical easy (synchronous) model was only fully understood in the mid 2000s.<ref name=DrosselRbn>{{cite book|last1=Drossel|first1=Barbara|editor1-last=Schuster|editor1-first=Heinz Georg|title=Chapter 3. Random Boolean Networks|date=December 2009|doi=10.1002/9783527626359.ch3|arxiv=0706.3351|series=Reviews of Nonlinear Dynamics and Complexity|publisher=Wiley|pages=69–110|isbn=9783527626359|chapter=Random Boolean Networks}}</ref>

The seemingly mathematical easy (synchronous) model was only fully understood in the mid 2000s.

The seemingly mathematical easy (synchronous) model was only fully understood in the mid 2000s.

A Boolean network is a particular kind of sequential dynamical system, where time and states are discrete, i.e. both the set of variables and the set of states in the time series each have a bijection onto an integer series. Such systems are like cellular automata on networks, except for the fact that when they are set up each node has a rule that is randomly chosen from all 2}} possible ones with K inputs. With K=2 class 2 behavior tends to dominate. But for K>2, the behavior one sees quickly approaches what is typical for a random mapping in which the network representing the evolution of the 2 states of the N underlying nodes is itself connected essentially randomly.

A Boolean network is a particular kind of sequential dynamical system, where time and states are discrete, i.e. both the set of variables and the set of states in the time series each have a bijection onto an integer series. Such systems are like cellular automata on networks, except for the fact that when they are set up each node has a rule that is randomly chosen from all 2}} possible ones with K inputs. With K=2 class 2 behavior tends to dominate. But for K>2, the behavior one sees quickly approaches what is typical for a random mapping in which the network representing the evolution of the 2 states of the N underlying nodes is itself connected essentially randomly.

布尔网络是一种特殊的顺序动力学系统，其中时间和状态是离散的，即时间序列中的变量集和状态集都具有对整数序列的双射。 这样的系统就像网络上的蜂窝自动机一样，除了以下事实：建立它们时，每个节点都有一个规则，该规则是从所有2个具有K个输入的可能节点中随机选择的。 在K = 2的情况下，第2类行为倾向于占主导地位。 但是对于K> 2，人们看到的行为迅速接近了随机映射的典型行为，在随机映射中，代表N个基础节点的2个状态的演化的网络本身基本上是随机连接的。

布尔网络是一种特殊的顺序动力学系统，其中时间和状态都是离散的，即时间序列中的变量集和状态集都各自有一个偏射到一个整数序列上。这样的系统就像网络上的细胞自动机一样，只是当它们被建立起来时，每个节点都有一个规则，这个规则是从所有2}}可能的规则中随机选择的，有K个输入。在K=2时，2类行为往往占主导地位。但对于K>2，人们看到的行为很快就会接近随机映射的典型特征，其中代表N个底层节点的2种状态演化的网络本身基本上是随机连接的。